Pith Number

pith:GCPYCS4O

pith:2016:GCPYCS4OVXGZZEEXNO7OWPJ4GB

not attested not anchored not stored refs pending

Burghelea conjecture and asymptotic dimension of groups

Alexander Engel, Michal Marcinkowski

arxiv:1610.10076 v3 · 2016-10-31 · math.GT · math.GR · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GCPYCS4OVXGZZEEXNO7OWPJ4GB}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:01:43.991703Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

309f814b8eadcd9c90976bbeeb3d3c30666d3b28bf084439c43d87d0dc2b27b8

Aliases

arxiv: 1610.10076 · arxiv_version: 1610.10076v3 · doi: 10.48550/arxiv.1610.10076 · pith_short_12: GCPYCS4OVXGZ · pith_short_16: GCPYCS4OVXGZZEEX · pith_short_8: GCPYCS4O

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GCPYCS4OVXGZZEEXNO7OWPJ4GB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 309f814b8eadcd9c90976bbeeb3d3c30666d3b28bf084439c43d87d0dc2b27b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d74955a3c91814dda02fd731ea9bdd4a3deb570079be42c62921ec0b20348e51",
    "cross_cats_sorted": [
      "math.GR",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-10-31T19:17:05Z",
    "title_canon_sha256": "1fc631c1639c36848d35727c5e2ca748f5e734b97df09db31983e4b032199e69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.10076",
    "kind": "arxiv",
    "version": 3
  }
}